Kempton Albee, Mike Barnes, Aaron Parker, Eric Roon and
A. A. Schaeffer Fry
Vol. 12 (2019), No. 4, 607–631
DOI: 10.2140/involve.2019.12.607
Abstract
Representations are special functions on groups that give us a way to study abstract
groups using matrices, which are often easier to understand. In particular, we are
often interested in irreducible representations, which can be thought of as the
building blocks of all representations. Much of the information about these
representations can then be understood by instead looking at the trace of the
matrices, which we call the character of the representation. This paper will address
restricting characters to subgroups by shrinking the domain of the original
representation to just the subgroup. In particular, we will discuss the problem of
determining when such restricted characters remain irreducible for certain low-rank
classical groups.
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